Arrange the following pentoxides in order of their increasing acidic strength.

A. \(Bi_2O_5\)

B. \(Sb_2O_5\)

C. \(P_2O_5\)

D. \(As_3O_5\)

E. \(N_2O_5\)

Choose the correct answer from the options given below:

A < B < D < C <  E

The correct answer is option 1. A < B < D < C <  E.

The acidic strength of oxides generally increases as we move from left to right across a period in the periodic table and decreases as we move down a group. This is because:

Electronegativity: Oxides of more electronegative elements are more acidic because they can better stabilize the negative charge on the oxide ion.

Oxidation State: Higher oxidation states usually lead to stronger acids as the central atom has a higher positive charge and can better stabilize the negative charge of the oxide ion.

Size of the Central Atom: Smaller central atoms have a higher charge density, which generally leads to greater acidic strength.

Let us analyze each pentoxide based on these factors:

A. \(Bi_2O_5\) (Bismuth Pentoxide)

Bismuth is an element of group 15 and the 6th period of the periodic table. Bismuth typically has an oxidation state of +5 in \(Bi_2O_5\). Bismuth is larger and has a lower charge density compared to elements in higher periods. This results in a weaker acidic character. Bismuth oxides are generally amphoteric or weakly acidic. The large size of bismuth reduces the ability of the oxide to stabilize the negative charge, resulting in lower acidity.

B. \(Sb_2O_5\) (Antimony Pentoxide)

Antimony is an element of group 15 and the 5th period of the periodic table. Antimony has an oxidation state of +5 in \(Sb_2O_5\). Antimony is smaller than bismuth and has a higher charge density. This makes its oxides more acidic than those of bismuth. Antimony's smaller size compared to bismuth results in a higher charge density, which increases the acidic character of its oxides.

C. \(P_2O_5\) (Phosphorus Pentoxide)

Phosphorus is an element of group 15 and the 3rd period of the periodic table. Phosphorus has an oxidation state of +5 in \(P_2O_5\). Phosphorus is smaller and has a higher charge density than arsenic. This results in stronger acidity for phosphorus oxides. The small size and high electronegativity of phosphorus result in a greater ability to stabilize the negative charge, making \(P_2O_5\) more acidic than arsenic pentoxide.

D. \(As_3O_5\) (Arsenic Pentoxide)

Arsenic is an element of group 15 and the 4th period of the periodic table. Arsenic has an oxidation state of +5 in \(As_3O_5\). Arsenic, being in a higher period than antimony, has a higher charge density than antimony and is more electronegative.  Arsenic's higher charge density and smaller size compared to antimony lead to a more acidic character for its oxides.

E. \(N_2O_5\) (Nitrogen Pentoxide)

Nitrogen  is an element of group 15 and the 2nd period of the periodic table. Nitrogen has an oxidation state of +5 in \(N_2O_5\). Nitrogen is the smallest and most electronegative among these elements. The high electronegativity and high oxidation state make \(N_2O_5\) very acidic. The small size of nitrogen and its high charge density make its oxides extremely acidic, leading to a very strong acidic character compared to other pentoxides.

Summary of Increasing Acidic Strength

\(Bi_2O_5\): Least acidic due to the large size of bismuth and its lower charge density.

\(Sb_2O_5\): More acidic than \(Bi_2O_5\) but less so than \(As_3O_5\) due to the smaller size and higher charge density of antimony.

\(As_3O_5\): More acidic than \(Sb_2O_5\) due to arsenic's higher charge density and smaller size.

\(P_2O_5\): More acidic than \(As_3O_5\) because phosphorus is smaller and has higher electronegativity.

\(N_2O_5\): Most acidic due to nitrogen's small size and high electronegativity.

Thus, the correct order of increasing acidic strength is: \(Bi_2O_5\) < \(Sb_2O_5\) < \(As_3O_5\) < \(P_2O_5\) < \(N_2O_5\).

So, the correct option is indeed option 1: A < B < D < C < E.